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curve #5887

y2 + xy = x3 + x2 − 824516263x + 7853600293093
a-invariants
[1, 1, 0, -824516263, 7853600293093]
c-invariants
[39576780649, -6785807479087157]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
48026417067330
discriminant (Δ)
9226146945300505271013315600
Faltings height
4.0905
naive height
73.2045
primes of bad reduction
2, 3, 5, 13, 37, 73, 173, 211, 1249
regulator
2298.4859299791346670395422550254139173064340149198
submitted by
The Wren
submitted at
last updated

Witness: 6 independent points log in to add more points →

Commentary

Source: Michael Rubinstein’s elliptic-curves-by-rank repository, torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz, 70th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz The source row reports proven rank 6 with torsion Z/2 × Z/2 and supplies these six generators on the minimal model. I checked all six points exactly and independently verified their independence. The full torsion group and both supplied torsion generators were checked separately. Conductor 48026417067330. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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